160sin^2xcos^2x. Use the​ power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1

Answer 1

So 160sin²(x)cos²(x) = 160•(1 - cos(2x))/2•(1 + cos(2x))/2 = 40(1 - cos²(2x))

Applying the power reduction formula again:

40(1 - cos²(2x)) = 40(1 - (1 + cos(4x))/2) = 40(2/2 - (1 + cos(4x))/2) = 20(1 - cos(4x)) =

20 - 20cos(4x)